Laser Scattering Calculator

Analyze laser light scattering from particles and aerosols using Rayleigh and Mie scattering theory. Essential for atmospheric optics, particle sizing, lidar applications, and optical diagnostics.

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Physics Note: Scattering regime depends on size parameter α = 2πr/λ. Rayleigh scattering (α << 1), Mie scattering (α ≥ 1), and geometric optics (α >> 1).

Input Parameters

Incident laser wavelength (typical: 200-10000 nm)
Spherical particle radius
n
Real part of refractive index (water: 1.33, glass: 1.5)
n₀
Surrounding medium (air: 1.0, water: 1.33)
degrees
Observation angle (0° = forward, 90° = side, 180° = back)

Scattering Analysis Results

Size Parameter
1.18
α = 2πr/λ
Scattering Regime
Mie
Theory
Cross Section
3.14 × 10⁻¹⁴
m²
Scattering Efficiency
2.15
Q_sca
Angular Intensity
0.75
I(θ)/I₀
Asymmetry Parameter
0.62
g

Scattering Theory

Size Parameter

α = 2πr/λ
α = Size parameter (dimensionless) r = Particle radius (m) λ = Wavelength in medium (m)

Rayleigh Cross Section

σ_R = (8π³r⁶/3λ⁴) × |m²-1/m²+2|²
σ_R = Rayleigh scattering cross section m = Relative refractive index Valid for α << 1

Mie Efficiency

Q_sca = Σ(2n+1)(|a_n|² + |b_n|²)
Q_sca = Scattering efficiency a_n, b_n = Mie coefficients Valid for all α values

Applications

Atmospheric Lidar

Analyze aerosol and cloud particle properties using backscattered laser light for weather monitoring and atmospheric research.

Particle Sizing

Determine particle size distributions in industrial processes, pharmaceuticals, and environmental monitoring applications.

Biomedical Optics

Study light scattering from biological cells and tissues for medical diagnostics and therapeutic applications.

Material Characterization

Analyze optical properties of nanoparticles, colloids, and suspensions in research and quality control.

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Frequently Asked Questions

What is the difference between Rayleigh and Mie scattering?

Rayleigh scattering occurs when particle size is much smaller than wavelength (α << 1), with λ⁻⁴ dependence. Mie scattering applies to all particle sizes and requires complex calculations.

How do I determine the scattering regime?

Calculate the size parameter α = 2πr/λ. If α << 1 (typically < 0.3), use Rayleigh theory. If α ≥ 1, use Mie theory. For α >> 1, geometric optics applies.

What affects scattering intensity?

Scattering intensity depends on particle size, refractive index contrast, wavelength, and observation angle. Smaller particles scatter more at shorter wavelengths.

How is this used in lidar systems?

Lidar measures backscattered light (180°) to determine particle concentration and size distribution. The calculator helps predict signal strength and optimize laser parameters.